The magnetic field inside the Earth's fluid and electrically conducting outer core cannot be directly probed. The root-mean-squared (r.m.s.) intensity for the resolved part of the radial magnetic field at the core–mantle boundary is 0.3mT, but further assumptions are needed to infer the strength of the field inside the core. Recent diagnostics obtained from numerical geodynamo models indicate that the magnitude of the dipole field at the surface of a fluid dynamo is about ten times weaker than the r.m.s. field strength in its interior, which would yield an intensity of the order of several millitesla within the Earth's core. However, a 60-year signal found in the variation in the length of day has long been associated with magneto-hydrodynamic torsional waves carried by a much weaker internal field. According to these studies, the r.m.s. strength of the field in the cylindrical radial direction (calculated for all length scales) is only 0.2mT, a figure even smaller than the r.m.s. strength of the large-scale (spherical harmonic degree n≤13) field visible at the core–mantle boundary. Here we reconcile numerical geodynamo models with studies of geostrophic motions in the Earth's core that rely on geomagnetic data. From an ensemble inversion of core flow models, we find a torsional wave recurring every six years, the angular momentum of which accounts well for both the phase and the amplitude of the six-year signal for change in length of day detected over the second half of the twentieth century. It takes about four years for the wave to propagate throughout the fluid outer core, and this travel time translates into a slowness for Alfvén waves that corresponds to a r.m.s. field strength in the cylindrical radial direction of approximately 2mT. Assuming isotropy, this yields a r.m.s. field strength of 4mT inside the Earth's core.